Last modified: 2014-03-28

#### Abstract

Many populations are subjected to external perturbations that increase or decrease their sizes independently of the underlying population dynamics. On one hand, increases in population size are linked to introductions of new individuals; the underlying causes may be natural, e.g. immigration, or related to human practices, e.g. reintroduction of species or biological control operations. On the other hand, decreases in population size are due to the removal of a fraction of the population, so that they are intrinsically dependent on the size of the population. Such takings may be natural, e.g. emigration, or caused by humans, e.g. harvesting, culling, etc... Both such perturbations may affect population dynamics continuously over time, but they can also happen abruptly, as pulses occurring at discrete time instants. The nature and magnitude of the perturbation, as well as its frequency when it is pulsed, can bring about significant changes in population dynamics. Therefore, it is important to develop a modelling approach that allows to compare different perturbation regimes for a given perturbation effort. Such a framework exists for perturbations that increase population sizes at constant rate, but it is still lacking for the state-dependent ones that decrease population sizes, i.e. perturbations linked to exogenous takings.

The present contribution aims at proposing a modelling technique that allows to compare, for a given taking effort, pulsed taking regimes that vary in frequency. In the limit of an infinite frequency of pulses, this framework also allows to compare pulsed and continuous taking regimes. We show that there are different ways to model such problems, each having its strengths and weaknesses. We illustrate our approach on several examples drawn from various fields of population dynamics, e.g. population dispersal, population harvesting or epidemic dynamics. In particular, we report how our findings fuel the debate over the respective efficacy of pulsed vs. continuous vaccination strategies.